Problem: Solve for $x$ : $5x^2 + 25x + 30 = 0$
Solution: Dividing both sides by $5$ gives: $ x^2 + {5}x + {6} = 0 $ The coefficient on the $x$ term is $5$ and the constant term is $6$ , so we need to find two numbers that add up to $5$ and multiply to $6$ The two numbers $2$ and $3$ satisfy both conditions: $ {2} + {3} = {5} $ $ {2} \times {3} = {6} $ $(x + {2}) (x + {3}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 2) (x + 3) = 0$ $x + 2 = 0$ or $x + 3 = 0$ Thus, $x = -2$ and $x = -3$ are the solutions.